A car on the cross road is moving towards east at a speed of 40km/hr. Another car which is 1 km south of crossing is approaching the crossing with the same speed . Their closest distance of approach will be ?

Question

Answer

Answer

Calculation of the Closest Distance of Approach between Two Cars on Cross Road

Given Information

Speed of the first car moving towards east = 40 km/hr

Speed of the second car approaching the crossing = 40 km/hr

Distance between the second car and crossing = 1 km

Calculation

Let's assume that the two cars meet at a point P which is the closest distance of approach.

Let's also assume that the first car takes t hours to reach the crossing from its initial position and the second car takes T hours to reach the crossing from its initial position.

Then, the distance covered by the first car = 40t km and the distance covered by the second car = 40T km.

Using Pythagoras theorem, the distance between the initial position of the second car and point P is given by:

√(1^2 + (40T)^2)

Similarly, the distance between the initial position of the first car and point P is given by:

√((40t)^2 + 0^2)

As the two cars meet at point P, the above two distances must be equal.

Therefore, we can write:

√(1 + 1600T^2) = 40t

Squaring both sides, we get:

1 + 1600T^2 = 1600t^2

Bringing all the terms to one side, we get:

1600t^2 - 1600T^2 = 1

Dividing both sides by 1600, we get:

t^2 - T^2 = 0.000625

Factoring the left-hand side, we get:

(t - T)(t + T) = 0.000625

As t and T are positive, we can ignore the negative solution.

Therefore, we can write:

t - T = 0.025

Substituting this value of (t - T) in the equation we got earlier, we get:

t^2 - (t - 0.025)^2 = 0.000625

Simplifying this equation, we get:

t =

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